The relationship between a multi-agent system dynamics and its corresponding graph properties is critical in terms of the network controllability and stability [1]}, [2]}. For a multi-agent network with one(multiple) leader(s), Rahmani et. al. established how the symmetry structure of a network characterized by automorphism group, relates to the controllability of such network. Tanner [3]} investigated the effects of network connectivity and size on its dynamic controllability in presence of a single leader, considering neighborhood based inter-connection topology structure. In multi-agent cooperative tasks, an increase in the network connectivity helps in faster convergence of the consensus [4]}. The author in [3]} derived sufficient conditions for the overall network controllability, and also showed that high connectivity may cause adverse effect on network controllability. In [6]}, the structural controllability problem of multi-agent network with single leader was investigated under switching topologies.
